Automorphisms and Isomorphisms of Symmetric and Affine Designs
William M. Kantor
DOI: 10.1023/A:1022416002358
Abstract
Given a finite group G, for all sufficiently large d and for each q > 3 there are symmetric designs and affine designs having the same parameters as PG( d, q) and AG( d, q), respectively, and having full automorphism group isomorphic to G.
Pages: 307–338
Keywords: automorphism group of symmetric design
Full Text: PDF
References
1. Babai, L., On the abstract group of automorphisms, in Combinatorics, Proc. Eighth British Comb. Conf. (ed. H.N.V. Temperley), Cambridge U. Press, Cambridge, 1981, pp. 1-40.
2. Dembowski, P., Finite Geometries. Springer, Berlin-Heidelberg-New York, 1968.
3. Dembowski, P. and Wagner, A., "Some characterizations of finite projective spaces," Arch. Math. 11 (1960), 465-469.
4. Frucht, R., "Herstellung von Grapnen mit vorgegebener abstrakter Gruppe," Compositio Math. 6 (1938), 239-250.
5. Jungnickel, D., "The number of designs with classical parameters grows exponentially," Geom. Ded. 16 (1984), 167-178.
6. Jungnickel, D. and Lenz, H., "Two remarks on affine designs with classical parameters," J. Comb. Theory (A)3{\tt>\hskip-.5e>} (1985). 105-109. KANTOR
7. Kantor, W.M., Exponentially many symmetric and affine designs (unfinished manuscript, 1967).
8. Kantor, W.M., "Dimension and embedding theorems for geometric lattices," J. Comb. Theory (A) 17 (1974), 173-195.
9. Kantor, W.M., "Symplectic groups, symmetric designs, and line ovals," J. Algebra 33 (1975), 43-58.
10. Kantor, W.M. (in preparation).
11. Mendelsohn, E., "On the groups of automorphisms of Steiner triple and quadruple systems,"J Comb. Theory (A) 25 (1978), 97-104.
12. Norman, C.W., "Hadamard designs with no non-trivial automorphisms," Geom. Ded. 2 (1973), 201-204.
13. Norman, C.W., "Nonisomorphic Hadamard designs,"
7. Comb. Theory (A) 21 (1976), 336-344.
14. Shrikhande, S.S., "On the nonexistence of affine resolvable balanced incomplete block designs," Sankhya 11 (1951), 185-186.
15. Todd, J.A., "A combinatorial problem,"
7. Math. Phys. 12 (1933), 321-333.
2. Dembowski, P., Finite Geometries. Springer, Berlin-Heidelberg-New York, 1968.
3. Dembowski, P. and Wagner, A., "Some characterizations of finite projective spaces," Arch. Math. 11 (1960), 465-469.
4. Frucht, R., "Herstellung von Grapnen mit vorgegebener abstrakter Gruppe," Compositio Math. 6 (1938), 239-250.
5. Jungnickel, D., "The number of designs with classical parameters grows exponentially," Geom. Ded. 16 (1984), 167-178.
6. Jungnickel, D. and Lenz, H., "Two remarks on affine designs with classical parameters," J. Comb. Theory (A)3{\tt>\hskip-.5e>} (1985). 105-109. KANTOR
7. Kantor, W.M., Exponentially many symmetric and affine designs (unfinished manuscript, 1967).
8. Kantor, W.M., "Dimension and embedding theorems for geometric lattices," J. Comb. Theory (A) 17 (1974), 173-195.
9. Kantor, W.M., "Symplectic groups, symmetric designs, and line ovals," J. Algebra 33 (1975), 43-58.
10. Kantor, W.M. (in preparation).
11. Mendelsohn, E., "On the groups of automorphisms of Steiner triple and quadruple systems,"J Comb. Theory (A) 25 (1978), 97-104.
12. Norman, C.W., "Hadamard designs with no non-trivial automorphisms," Geom. Ded. 2 (1973), 201-204.
13. Norman, C.W., "Nonisomorphic Hadamard designs,"
7. Comb. Theory (A) 21 (1976), 336-344.
14. Shrikhande, S.S., "On the nonexistence of affine resolvable balanced incomplete block designs," Sankhya 11 (1951), 185-186.
15. Todd, J.A., "A combinatorial problem,"
7. Math. Phys. 12 (1933), 321-333.